Essentially, Arya Stark clearly disregards traditional medical advice (to take an apple a day), and resultantly, requires a doctor. Not a particularly interesting case at surface level, but lets go deeper, and peek at the injuries sustained...

The injury

We are shown a dagger slash across the lower abdomen, followed by a stab to the hilt of this blade, and a further stab where the knife is then twisted at least 90 degrees.

The weapon

The knife is an estimated 4" blade, at over double the length of the Waif (the stabber)'s closed hand when holding it. The slash is hidden by the camera angle, making depth of injury difficult to guesstimate, but the knife is buried to the hilt during the two stabs. The Faceless Men are known to use poisons, and so it wouldn't be a stretch to imagine the blade was coated with something nasty too.

The wounds

We have 3 wounds to consider. One potentially, and two definitely, involve 3 layers of tissue: the skin, muscles beneath, and the organs under that. I divide it up like this not because I love drawing it all out (okay, it's partly because of that), but mostly because damage to each has different acute and longer term consequences.

Skin

Holes in the skin interrupt the waterproof barrier that keeps nasty organisms out. Inflammation at the injury site provides a nutrient rich culture medium for healing, or for bacteria to thrive if present. The latter would rapidly allow life threatening infection to develop. Arya's escape into dirty (potentially sewage water), is a perfect opportunity to kickstart this process.

Muscle

Arya's slash wound looked deep enough to have gone through the rectus abdominis (the '6 pack') muscles of the abdomen, which (allegedly) lie beneath a layer of fat most of us know all too well. I think we can assume the abdominal wall muscles have been divided at least partially. This would affect their function, impairing Arya's core stability, which is needed for balance, and the parkour she miraculously then partakes in across the streets of Braavos..

Guts

All three wounds involve the abdomen, which is home to some important bits and pieces. They overlay the appendix, caecum (connection between small and large bowel), and potentially bladder, right ovary, and uterus. Damage to these mean that in addition to introducing infection, blood loss, and functional impairment; there is now potentially early (liquid) poop, late (solid) poop, and urine leaking around the wound into the abdominal cavity.

Early poop is full of chemicals to help break down digesting food into nutrients we can absorb. Like urine, acts as an irritant to the tissue it contacts. Formed poops later in the large bowel are full of bacteria, a ready loaded source for overwhelming infection to develop from. Fixing these structures to contain the problem would require some big surgery in a sterile environment. A surgeon would potentially want Arya to get a blood transfusion if she had bled out too much (which can cause things like heart attacks left untreated); antibiotics to prevent/treat infection; and advise minimal parkour.

Adhesions

In the longer term, even given perfect modern surgical conditions: adhesions (scar tissue) can form between structures in the abdomen after ANY surgery or deep injury has occurred. This 'sticks' bits of organs together with stringy scars. Organs which are usually mobile like the small intestines, can get tied up amongst the adhesions and cause 'obstruction'. This twisting blocks the transit system, causing digesting foods to 'back up', leading to a bloated abdomen, nausea, vomiting, and the inability to poop or pass wind (known as 'absolute constipation').

This is a life threatening medical emergency if the blood supply is also cut off in the twisted bowel, as without blood the tissue quickly dies and breaks down, resulting in leakage of bowel contents, bleeding, and potentially death.

Conclusions

Arya's injuries are serious. They would have required more medical aid than she received to survive. Game of Thrones has a really smart audience, so I doubt it was just me who's suspension of disbelief was shattered when she started jumping around a few minutes later. Maybe it's all for a wild sub plot where Arya wasn't the one who got stabbed.. or maybe she did die, and now someone's wearing her face (remember she did tell the Waif everything about herself earlier..). Honestly though, I'm just glad she survived for Season 7 to continues her path of vengeance..